It's something that used to be done a lot in the past back home (Iceland) since in the time before proper roads, bridges and cars the horses were the only way to get around. There are a bunch of rivers that are too deep for the horses to just walk over so they had to swim over with people on their backs.
It's not really done seriously anymore, but some people do it for fun. You need a strong steady horse and to teach them not to panic in the water and to keep going. A horse with a good water sense used to be really highly prized back then since you were trusting the horse with your life and it's dangerous going over water like that.
I've never done it, most of the deep rivers have heavy currants and it's dangerous to cross, in addition to being glacial rivers and very cold *brrr* I went riding with a bunch of tourists and a guide several years ago though and as we went past a lake the guide went into the lake to show the tourists how it was done.
He invited me to try it too but the lake was very cold so I wasn't going to.
I took a pic though:
So yeah, has anyone here done this sort of thing?